Comment on "Numerical estimates of the spectrum for anharmonic PT symmetric potentials" by Bowen et al

TL;DR

This paper critiques a previous study by Bowen et al., emphasizing the importance of understanding the physics and mathematics behind numerical methods to avoid flawed conclusions in spectral analysis of PT-symmetric potentials.

Contribution

It highlights the pitfalls of rushing into numerical studies without proper understanding, correcting misinterpretations in Bowen et al.'s flawed numerical work.

Findings

Bowen et al.'s numerical methods were incorrectly applied.

Misinterpretation of the spectral results led to incorrect conclusions.

Rigorous verification of Bender and Boettcher's work remains valid.

Abstract

The paper by Bowen, Mancini, Fessatidis, and Murawski (2012 Phys. Scr. {\bf 85}, 065005) demonstrates in a dramatic fashion the serious difficulties that can arise when one rushes to perform numerical studies before understanding the physics and mathematics of the problem at hand and without understanding the limitations of the numerical methods used. Based on their flawed numerical work, the authors conclude that the work of Bender and Boettcher is wrong even though it has been verified at a completely rigorous level. Unfortunately, the numerical procedures performed and described in the paper by Bowen et al are incorrectly applied and wrongly interpreted.